CAPF AC 2021 Q76: General Mental Ability – Quantitative Aptitude
In a stock clearance sale, a shopkeeper gives 40% off on all his items. He incurs a loss of 25% by selling an item of marked price ₹2,000. Which one of the following is the cost price of this item?
- (a) ₹1,800
- (b) ₹1,200
- (c) ₹1,600
- (d) ₹1,400
Answer: (c) ₹1,600
Explanation
Discount and loss together
Given: a shopkeeper gives 40% off on a marked price of ₹2,000 and still makes a loss of 25%; find the cost price.
How to think: work in two steps.
First find the selling price from the marked price.
Then find the cost price from the selling price.
| Step | Working |
|---|---|
| Discount | 40% of 2,000 = 800 |
| Selling price | 2,000 − 800 = ₹1,200 |
| Loss of 25% | Selling price = 75% of cost price |
| Cost price | 1,200 ÷ 0.75 = ₹1,600 |
Check: 25% of 1,600 is 400, and 1,600 − 400 = 1,200.
Answer: (c) ₹1,600.
Why each option is right or wrong
- (a) Incorrect. With a cost of ₹1,800, selling at ₹1,200 is a loss of about 33%.
- (b) Incorrect. ₹1,200 is the selling price, not the cost price.
- (c) CORRECT. 1,200 is 75% of the cost price, so the cost price is ₹1,600.
- (d) Incorrect. With a cost of ₹1,400, the loss would be only about 14%.
Key point
Selling price = marked price × (1 − discount). Loss% is on cost price: selling price = cost price × (1 − loss%). So cost price = selling price ÷ (1 − loss%).
Remember
Loss is always counted on the cost price.
Common mistakes
- Taking 25% of the selling price (₹300) and adding it to get ₹1,500.
- Stopping at the selling price of ₹1,200 and marking it as the cost.
- Applying the loss percentage to the marked price instead of the cost price.
Exam tip
Educated guess: there is a loss, so the cost price must be more than the selling price of ₹1,200. That removes (b). Then test ₹1,600: a quarter of it is 400, and 1,600 − 400 = 1,200.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (discount, profit and loss)
- R. S. Aggarwal, Quantitative Aptitude — Profit and Loss